A dynamic model for continuous adiabatic drying

A DYNAMIC MODEL FOR

CONT

I

NOUS

ADIABATIC DRYING

by

DAVID ANTHONY CAMPANELLA

SUBMITTED IN PARTIAL FULF

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OF THE REQU

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DEGREE OF BACHELOR DF

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MASSACHUSETTS

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TECHNOLOGY

June

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TABLE OF CONTENTS Page i List of Figures ₃ ii Acknowledgement 4 I Abstract ₅ II Introduction ₆

III _{The Background of Drying 9}

IV The Dynamic IModel 12

IVa Energy Balance on The Gas Stream 15

IVb Moisture Balance on The Gas Stream 21 V Dynamic Simulation and The Results 24

Va Time Dependents ₂₅ Vb Optimizing Velocity 28 Vc Temperature Flucuation ₃₀ VI Conclusion ₃₂ VII Nomenclature ₃₄ VIII Appendix ₃₅ IX Bibliography ₄₃ (2)

IIST OF FIGURES

Page

Temperature Difference Control

Dynamic Control

Conveyor Belt Drier

Mathematical Model

Detailed Unit Cell Flow in Unit Cell

Flow Charts Time Dependence Optimizing Velocity Temperature Flucuation

(3)

3

4

5

6

9

V-Dedicated to my parents

I would like to thank Babu Joseph for his help in formulating this dynamic model. And a very special thanks to Joanne Rudinsky for the many long and late hours spent typing this manuscript.

I. ABSTRACT

In this thesis, I intend to find the dynamic equations which will predict the outlet temperature of a continuous dryer. Dynamic equations determine the steady state condi-tions and how quickly a new steady state is reached with small perturbations. The main purpose of this dynamic model is to know how to change the inlet conditions so that the desired outlet moisture content is continuously maintained. By knowing the temperature profile and the final outlet temperature, it will be possible to predict the outlet

moisture content in the gas stream and in the product stream. As inlet temperatures change, this set of equations will

predirt the changes in the outlet conditions. That is, gas temperature, gas moisture coitent, and solid moisture content. The desired changes in the inlet conditions can be determined from the difference of the predicted out-let conditions and the desired outout-let conditions. The dynamic equations predict both the change of the para-meters at each position in the dryer and also the changes in each position with the change of time.

II. INTRODUCTION

Today with energy being a vital resource, engineers are looking for ways of conserving energy by making pro-cesses efficient. In a drying operation it would be ideal if just enough energy was used to dry a product to its desired moisture content. Just heating up a product until it is dry could be wasteful and disastrous. Some products can only be dried to a certain critical level. Beyond this level, the products would be ruined; but, if you didIt dry it enough, you have to dry it again. This is a waste of process, time, and energy for products that

are sensitive to moisture content.

It will be possible to control the moisture content of the product stream to the desired level in the model that I am proposing. This model will be able to be used on

adiabatic continuous drying operations. So far, only a co-current flow model has been developed. Essentially, this model comes from an overall energy balance and a moisture balance on the air stream and on the product stream.

Three dynamic equations are derived from these three balances. The dynamic temperature equation will make it possible to determine the temperature profile and how it changes with time. Then, the moisture content in the gas stream can be calculated. As the temperature changes with position and time, the evaporation rate will also vary with

Position and time. Using the dynamic temperature profile, the dynamic moisture content in the gas and solid stream can be determined. The moisture in the solid stream is calculated from the steady state equation derived from the

solid stream moisture balance.

One of the problems in making this model is that the moisture content of the solid product stream cannot be measured directly. To get an exact measure on the dryness

of the product, it would be necessary to analyze individual samples of the product stream. The time which it takes to analyze the exact moisture content of the product stream would make it impossible to maintain continuous operation. Under certain conditions and assumptions, the product

mois-ture content can be measured indirectly.

The indirect way of measuring the moisture content on solids is by knowing the temperature of the gas stream

in which the solid is in equilibrium with. Through psychro-metic considerations, the humidity of the gas stream can be calculated. The difference between the dry-bulb

temp-erature and the wet-bulb temptemp-erature is proportionately

related to the difference between humidity at saturation and the humidity of the gas. The dry-bulb and wet-bulb temp-eratures can be easily monitored in a continuous dryer. Thus, the moisture content of the gas stream can readily be measured. Then the moisture in the product stream can be estimated by using an overall moisture balance.

There are three different rate of drying zones. The first is the drying of excess water. This is when the solid particles are essentially floating in a stream of water. Water from both the particles and the liquid stream are being evaporated into the gas stream. The drying rate is independent of the solid particles and only depends on the heat of vaporization. The second zone is essentially known as the constant drying rate zone. This is when the complete surface of the particles are wet. Drying takes place evenly on all surface areas. The third zone is when parts of the surface are dry. Now the drying rate decreases

since drying is taking place on the surface and through diffusion. This is known as the falling drying rate zone.

The transition between the constant rate zone and the falling rate zone takes place at the critical moisture content designated by (XC). The major concern of this model is the drying of particles to this critical moisture

level. My proposed model deals with the adiabatic drying in the constant rate zone. Under adiabatic conditions, the wet-bulb temperature is constant. At equilibrium, the surface temperature of the particles is the wet-bulb temp-erature. It is at this temperature that evaporation takes place. The difference between the dry-bulb temperature

and the wet-bulb temperature is the driving force of the evaporation.

III. THE BACKGROUND OF DRYING

In the paper industry, textile industry, food industry, and pharmaceutical industry there are many products which need to be dried to specific moisture content. In these

fields, the product can be irreversibly damaged by

over-drying. In 1973, the Sira Institute developed new techniques for measuring moisture content of materials continuous and batch drying processes. F. C. Harbert developed a

control-ling technique based on the measurements of temperature differences. His method is suitable for measuring any moisture content less than that to saturate the material.

In the Harbert method, the temperature of the drying mat-erial and the wet-bulb temperature are compared. For each material, specific temperature differences were cor-related to specific moisture contents. In a process dev-eloped for the continuous drying of cloth fabric the mon-itoring of i'the temperature difference between the fabric and the wet-bulb temperature determines at what speed the fabric is drawn through the dryer, (See fig. 1, below).

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In any continuous drying operation, the inlet condi-tions will inevitably vary to some degree. This will cause the outlet conditions to also vary. It is desired to know how to adjust the inflowing air to account for the variance

in the flow of the material being dried so the outlet

moisture content will be constant. The purpose of a dynamic model is to know how to vary the adjustable inlet parameters

so the product stream will be at the desired value. (See fig. 2, page 11.)

In continuous dryers the variable parameters are the flow of the material to be dried, the flow rate of the drying gas, and the temperature of the drying gas. Once a set of equations describing the drying process of a

particular drying unit is known, the affect of varying the parameters can be determined. _{The flow rate of the gas} and temperature of the gas are dependent on each other. Increasing the flow rate will cause the temperature of the gas to drop. _{This would depend on the air heating system} and is not a concern of this model.

In order to control a drying process, some parameters must be monitored to determine how the inlet conditions must be varied. _{The desired result is a product with a}

part-icular moisture content. _{In many cases, this moisture} con-tent cannot be measured directly. Nor, can its temperature be measured directly. But, the properties of the air which

it is in contact with can be measured and monitored. The two parameters that can be-instantaneously measured are the

dry-b ulb temperature and the wet-builb temperatures. From

the dry-bulb and wet-bulb temperatures, the moisture content of the out flowing air can be determined. Calculating the differences between the incoming moisture of the solid and the outgoing moisture of the gas stream, will give a reasonable approximation of the moisture content of the

solid product stream. Through the dynamic equations for the dryer, the degree in which the inlet parameters should be changed can be calculated.

GAS DC-TecTOK

fig7ure 2

IV. THE DYNAIC RMODEL

A model for drying solids moving on a conveyor belt or tray-type drier, is now proposed. (See fig. 3, page 12) The drying air is blowing in the same direction as the

solid is moving. It is in this model that no energy is lost to the drying apparatus. All heat transfer is to the solid being dried. This model does not account f'rr

the pre-heating zone. Nor, does this model cover the falling rate drying zone past the critical moisture con-tent. The rate of evaporation is related to the rate of heat transfer from the gas to the solid. The rate of drying can be given as a ratio of diffusion to heat transfer. In the model studied here, the main mode of heat transfer is conduction.

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The continOus conveyor drier is rcepresented by a

gas stream flowing at a velodity V and a solid stream moving at a slower speed S. (See fig. 4) The length

of the drier is divided into (N-1) compartments of equal

size.

The Mathematical Model

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V = Velocity of gas through drier (ft/hr)

S = Speed which solid moves through drier (ft/hr)

(N-1)= Number of unit cells in the drier

DZ = Length of unit cell (ft)

figure 4

(113)

C, t~

A mass and energy balance is written for one compar't-ment to lead to a set of differential equations for the

drier. The differential equations come from letting the limit of the length of each compartment go to zero. The imput of the compartment or unit cell is subscripted with N. _{The output side is subscripted (N+1). (See fig.5)} The length is delta Z, represented by DZ in the computer program. The width is W. The area perpendicular to the flow of the gas and the solid are represented by AG and AS respectively.

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AG

N N+1

Solid flowing into the page

Solid flowing to the right

AG Cross sectional area perpendicular to gas flow

AS Cross sectional area perpendicular to solid flow W'DZ Area of gas-solid interface

IVa. The Energy Baance on The Gas Stream

The gas is assumed to be in plug flow. The accumu-lation of energy in the unit cell per unit time is equal to the difference of the input and the output of energy. The heat content of the moisture is ignored here:

Accumulation = Input - Output (1)

Accumulation is equal to the change of heat content per unit time. The units are BTU's per hour. The volume

of gas is the cross secional area times the length, (AG-DZ). The mass is the volume times the density of the gas, (DENG). The mass equals (AG-DZ-DENG). The heat capacity of the

gas is CPG and the temperature is taken at the outlet of the unit cell. The partial derivitive equation for the

accumulation of energy is:

Accumulation = (AGDZ-DENG-CPG-TG(N+1)) (2)

The input of energy into the cell is from the gas

flowing in. The volume per unit time is the velocity times the cross-secional area, V-AG. The temperature of the

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TG(N) = Dry-bulb gas temperature at the inlet (OF) TG(N+1) = Dry-bulb gas temperature at the outlet (OF) DENG = Density of the gas (lb/cu.ft)

CPG = Heat capacity of the gas (BTU/lbOF) Q = Heat transfered per unit time (BTU/hr)

figure 6

incoming gas is TG(N). Volume times density times heat capacity times the temperature gives the energy per degree per unit time. (See fig. 6 above)

Energy Input = (V-AG-DENG-CPG-TG(N))

(16)

The output of energy is from the outflowing gas and the heat transfer to the solid stream. The flow output

is similar to the input except the temperature is TG(N+1)

which is lower than TG(N) since sensible heat has been transfered to the solid stream. The heat transfer per unit time is designated by Q. (See fig. 6, page

P)

Energy Output = (V-AG-DENG-CPG-TG (N+1)) + Q (4)

The heat transfer to the solid stream calculated by use of a heat transfer coefficient, h.2 The rate of heat flowing across the solid-gas interface depends on the area of the interface and the driving force which is the temp-erature difference. The temperature difference is the gas temperature minus the temperature of the solid which is at the wet-bulb temperature, (TW). The area of the solid-gas interface is the length times the width, DZ-W. The units of the heat transfer coefficients are BTU per square feet per hour per degree Fahrenheit. The heat transfer to the drying solid:

Q = h-DZ-W-(TG(N+1) - TW)

(5)

The heat transfer coefficient can be correlated from the mass flow rate of the gas. The mass flow rate desig-nated by G is equal to the velocity times the cross-secional area times the gas density, G = V-AG-DENG. The heat

transfer coefficient is proportional to the mass flow rate raised to the eight tenths power (3)

h = 0.01-CO.8

(6)

Substituting equation 5 into equation 4 and equations 2,3, and 4 into equation 1 forms the transient energy

equatin:

(AG,:Z-DENGCPG-TC(N+l)) =

(TG(N)-TG(N+1))(V-AG-DENG-CP)-h-DZ-W(TG(N+I)-TW) ₍₇₎

Dividing by constants on the left hand side, (AG-DZ-DENG-CPG), and taking the limit of delta Z as it approaches 0 as N

approaches infinity leads to the following partial dif-ferential equation:

(TG(N+1)) = (TG(N) -

TO(N+1))-V

t Z AG.DENG.CPG

For non-adiabatic drying, which is not concerned in this model, the wet-bulb temperature (TW) would be calculated from the psychrometric equation. The dry-bulb temperature, the moisture content, and the moisture content in vapor pressure at saturation would have to be known.

The partial differential equation, (8), can be ap-proximated by a finite different equation: From the

finite different equation a FORTRAN equation for the gas temperature at each position along the dryer can be

determined.

The partial differential of temperature with respect to time can be approximated by the finite difference of the temperature at the same location at the beginning and ending of a time unit divided by that time unit, DT. The superscript, i, is the beginning of the time unit, and the superscript, i+1, is the end of the time unit.

t(i+1) = t(i) + DT (9)

TG(N+1) = TG(N+1)i+1 - TG(N+1)i (10)

t DT

Now equation

TG(N+1)i+l - TG(N+1)' DT

- TG(N+1)'+')__+

DZ

Solving for TG(N+1)i+1

h-W(TW-T(N+1)'+1

A.G -DENG *CPG

equals the following after re-arrangement and factoring to a common denomination:

TG(N+1)i+l = (TG(N+1) .GZ)+(TG(Ni+l-VT)+(TW.ZW)) (GZ+VT+ZW) Where GZ = AG-DENG-CPG-DZ VT = V.AG.DENG.-CPG+D. ZW = DZ-DT-H-W (12) (8) becomes: (TG(N)i+1

~b. The ioisture Lalance on The Gas Stream

The accumulation of moisture in the gas stream in the unit cell is equal to zero at all times since all moisture is carried out in the gas flow. The moisture carried in by the gas flow plus the amount evaporated into the gas stream is equal to the amount flowing out of the unit cell. The moisture flowing in equals the mass flow rate times the fraction of water to air, Y(N). The rate of evaporation corresponds to the heat transfer to the

solid stream divided by the latent heat of evaporation at the wet-bulb temperature. The amount of water flowing along the solid-gas interface must also be taken into account. The conservation of moisture in gas stream. and the solid-gas interface per unit time is:

G-Y(N) + (S'W-h-TEIMP-DT)/HV = G.Y(N+1) (13)

TEMP = (TG(N)) + TG(N+1))/2 - TW (14)

Where TEMP is the average dry-bulb temperature of the cell minus the wet-bulb temperature which is the driving force for the evaporation rate. Rearrange the above

equation and substituting for G leads to this equation

which can be translated directly into FORTRAN.

Y(N+1) = Y(N) + (S W-h-TEMP -DT)

( THM- VG -AG -DENG) (15)

The moisture in the solid stream can be calculated from the total moisture balance since the moisture on the gas stream is now known. The total moisture balance states that the difference of the moisture content in the gas

stream equals the moisture difference in the solid stream. Mass is conserved. The flow of moisture in per unit time

equals the mass flow rate times the fraction of water in the gasstream at the inlet. The fraction of water at

the outlet in the gas stream is higher than the iflet. The

moisture carried in the solid stream is the mass flow rate times the fraction of water per ttal amount water

saturation. The mass fraction is designated by X(N) and X(N+1) at theJinlet and outlet of the unit cell respec-tively. The mass flow rate for the solid stream is the mass velocity times the cross-sectional area perpendicular to the flow times the solids density. The mass flow rate equals S-AS-DENS. The conservation of moisture equation is:

(16)

The miure at the oule w. th it cill i:

X(N+1) = X(N) + (Y(N+1) - Y(N))(V-AG'DENG) ₍₁₇₎

(S-AS-DENS)

Equations 12, 15, and 17, model the change of gas

temp-erature, gas moisture content, and product moisture con-tent ---for each position in the drier as the time changes.

V. DYNAMIC SIMULATION AND THE RESULTS

With the aid of a digital computer, equations 12,

15, and 17, wei used to simulate the values of the gas

temperature, the gas moisture content, and the solid moisture content. The transient profiles for the gas temperature (TG) gas moisture content (Y), and solid

product moisture content (X) were studied for three cases. First, the variance of these profiles with time were determined at different fixed initial conditions. A

description of this program is in section Va. Steady state was attained very quickly. From start up, the slowest that steady state was reached was 10 minutes. After 6 minutes, 85 percent of the steady state condition had been reached. In most cases, steady state was

reached in under 5 minutes.

Next, the gas flow rate was optimized. The op-timal gas velocity was found within 0.02 ft. per sec. From this study it is apparent that flucuations in gas flow rate will have very little effect on the steady

state condition. The method of iteration is described in section Vb.

Third, the effect of flucuation of inlet temperature was simulated. A new steady state is reached in less than

a minute. For an instantaneous change of 200_{F causes the} product mbdsture content to vary by 1.2 percent. This is a very drastic change in-tmperature and only a slight

change in moisture content. Five degreeFahrenheit only cause the product moisture content to vary by 0.5 percent. Section Vc describes how equations 12, 15, and 17, were grouped to simulate the flucuation of temperature. The optimized steady state condition from the secod case was used as he initial condition at all locations on the drier.

From the three different simulations, the steady state was found to be stable. Small flucuations in the drying gas properties have very little effect on the steady state coiditions.

Va. Time Dependents

At the beginning of all simulatioq, the iitial conditions must be loaded. There are five types of

constants which are unique for any drying process. There are the characteristics of the drier, physical properties of the gas, physical properties of the solid to be dried, the energy used, and the speed of operation of the drier. The characteristic of conveyor driers are its length, cross-sectional area and its width.

The physical properties of the drying gas are its density, heat capacity, and initial moisture content. The

density is used to calculate the mass flowing into the drier. The heat capacity is the amount of energy brought in per unit of mass. The moisture content is the ratio

of the amount of water per mass to the amount at saturation.

The heat capacity for the solid is not needed. The energy balance was on the gas and water in the drier. Under the assumption that the solid is at the wetQbulb tempera-ture and that the wet-bulb temperatempera-ture is constant the energy balance on the solid stream is zero. The needed physical properties of the solid are its density and

moisture content. The cross-sectional area perpendicular to the direction of flow is needed to calculate the mass flow rate.

The energy properties are the dry-bulb temperature and the wet-bulb temperature. The hat of vaporation is a function of the wet-bulb temperature.

The time variables are the gas velocity, the solids

feed speed, and the unit time set to be used in calculathns. The values for TG, Y, X, for each position in the

drier need to be stored before calculation can be

performed. The number of positions used was 100. This means there are 99 unit cells. At the starting time, All positions are given the initial values.

To save calculation time, the constant that arises from the mass and energy balances are performed.

Now, the transient calculation can be performed. For a more detailed description of these equations and how they are processed, see the Appendix. First the time counter is set. Then the position counter is set. Now the transient profile for temperature and moisture

Time dependence

Begin

Read DL:,AG,Wi; DENG,CPGO(C; DET7SAS,XC;V,S,DT; V,TAW,T 0 o TG(K), Y(K) ,K DZ GA S ,ZT G,H, H,GZ ,VT,Z pOsF1)oT TG(N) Y(N) X (N)

~$It

EN

Vb. Optimizing Velocity

A third iternative loop can be added before the

time and position loop described in the previous section. A trial and error method is used to find the optimal gas flow velocity. The steady state for the new velocity is tested against the ideal case. The error determines whether a faster or slower velocity should be used. The ideal case is. to have the desired moisture content on the solid stream attained in the last unit cell. The flow chart for this program is given on the following page. See flow chart B.

Plow har ~c; ii Opt :ilzri~r ~ve I _{~ C I LV}

.Begin

//Read: D. AG,W; DENG,CPIG,YO D)ElNS,AS,XO; V,S,DT; HV,TW,T K 4-00 TGK),ty(K),X(K NVC Counter) ADZAS,ZT,,HT-W GZ pV'TZW IS Pstion TG(N) Y(N) X(N) X(N)X 9 =+ 10 0 bKV=V-1 00 TG(5) Y(5) (29) vel.cIy

Vc. Temperature Flucuation

Now that optimal operating conditions are known, they can be used as the initial value at all locations in the drier. After this has been stored, new energy values are read. These are dry-bulb temperature, bulb temperature, and the heat of vaporization at

wet-bulb temperature.

The new temperature, TG, is read into the first unit cell. Then values for the next cell are calculated

using the set of dynamic equations. After the values in the last cell are determined, the changes in the inlet conditions can be found using a similar approach as that given in section Vb. The flow chart for the dependence

of temperature on steady state is given in flow chart C.

Temperature Dependence

Read DL,AG,W; DENGCPGYO; DENSASXO; V,S,DT

r

(3

2)

VI. CONCLTUSION

Based on the stability ol the steady state condition, it would be feasible to maintain a continuous

conveyor-type dryer at a desired output be ihoitoring its temperature. When a flucuation in the temperature at a given point of

the dryer is detected, the effect on the outlet moisture content can be calculated. The changes in inlet conditions which are needed to get the outlet conditions back to the

desired level can be determined nearly instantaneously with the aid of a computer. These changes can be initiated

almost immediately and with a second calculation-can be

compared to the observed values. In this matter, the desired outlet condition can be maintained at the desired values. Large flucuations in inlet conditions will be very small by the time they reach the end of the dryer with the aid

of these continuous corrective measures. On a real dryer, terms for heat loss from the dryer and non-adiabatic

drying would have to be determined experimentally. These terms would be incorporated to this proposed dynamic model,

enabling continuous operation to be automatic.

If there is flucuation in the incoming moisture content of the solid stream, this would cause changes in gas temperature and wet-bulb temperature that could be detected when the solid reaches equilibrium with the gas at some point in the dryer. This is assuming that the

solid stream is in the dryer long enough to reach equili-brium with the gas stream. Monitoring the gas temperature

and the wet-bulb temperature should make it possible for

the dryer to be controlled automatically.

VII. NOI'MTENCLATURE

A - = Cross-section area perpendicular to gas flow(sq.ft) AS = Cross-section area perpendicular to solid flow(sq.ft) CPG = Heat capacity of the gas stream(BTU/lb0F)

CPS = Heat capacity of the solid stream(BTU/lb0 F) DENG = Density of the gas(lb/cu.ft)

DENS = Density of the solid(lb/cu.ft) DT Time step(hr)

DZ = Length of unit cell(ft)

G = Mass flow rate(lb/hr)(V-AG-DENG)

h = Heat transfer coefficient(BTU/sq.ft.hr9F) HV = Heat of vaporatization(BTU,/lb. H20)

Q = Heat transfer per unit time(BTU/hr) TG(N) = Dry-bulb temperature of gas at N.(OF) TW = Wethbulb temperature(OF)

S = Speed which solid moves through drier(ft/hr)

V = Velocity of drying gas through drier(ft/hr)

W = Width of drier(ft)

VIII. APPENDIX

STEADY STATE CROFILES

i t0 2.C 1 1 so 40 ~tr3(, Sb (A |t 50 _'Of TEPERATUR 2 5 0 g-338 oTP-I MJirOISTUjRE I .4 101 50 MOISTURE IN 7. C)

N THE GAS STREAT!

THE PRODUCT STREAH

Steady state reached in 6 minutes.

V= 74800. ft./hr. S= 100. ft./hr. XC= '0.01 water/water at saturation 1.0 ft. AS= 0.175 sq.ft. DENG= 0.0107 lbs./ cu. ft. CPG= 0.24 BTU/lbs. TW= 110. 0_F AG= 1.0 sq.ft. DENS= 84.1 lbs./cu.ft. DL= 10.0 ft. HV= 1034.1 BTU/lbs water TG(1)=250. F

(35)

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PROGRAM A T IM!E DEPENDENCE

CONT INOUS DR Y ING UNDE R AD I ABA T I C COND I T ION DIM ENSION READ CHARACTERI READ CHARACTERI READ CHARACTERI READ CHARACTERI READ CHARACTERI TG ST CS Cs ST CS READ (2,100) READ (2,100) READ (2,100) READ (2,101) READ (2,100) C IN ITIATE ARRAYS N DO 20 K=l110 TG(K)=T Y (K) =YO (100 ),Y(100),X(100)

ICS OF DRIER voDLoAG

OF IN FLOWING GAS DENGoCPGoYO

OF IN COMING SOLID DENSoASqXO

ICS OF TIME-VELOCITY VOSODT

OF THE ENERGY (TEMPERRATURE)

D L oAGs ,V

DENGoCPGsY0

DENS#ASqXO

VoSoDT

HV9TWT

ITH INITIAL CONDITIONS

0

X (K ) =XO

20 CONTINUE XC= 0.01

C CRITICAL MOISTURE CONTENT XC

C CALCULATE NEEDED CONSTANTS FOR CALCULATIONS

DZ=DL/99.

C PROPERTIES OF THE GAS STREAM DENSITY oHEAT GAS=AG*DENG*CPG ZT=DZ*DT G=AG*V*DEN% H=0 4 01*G**0 . 8 H Y1j H *'v GZ=GAS*DZ VT=DT*V*GAS ZW=ZT*HW. C RATIO OF MOISTURE VS= (V*AG*DENG) WRITE (3,800) WRITE (3,400) WRITE (3,401) WRITE (3,402)

IN GAS AND SOLID

/ (S*AS*DENS) DT ,DZ DLoAGoASoW DENGoCPGtYOsToTW HVTWT CAPACTIYoAREA FLOWS sHV C C C C C C

PAGE 2

WRITE (3 ,403 V ,S XO oXC ,DENS

WR ITT (3s404) GAS ,ZTqGH9H! 'GZqVTqZWPVS WRITE (3,405) D0 30 ITX=Iol5 00 90 1=199 lj= I + i TG ( J )= TG ( J) *GZ) + (TG( I) *VT) + TW*ZW )/( Z+VT+ZW) T EMP TG(I)+TG(J))/2.-T W

Y ( J )=Y ( I) + ( S*HW*TEMP*DT) / ( HV*AG*DENG*V) ) X(J)=X(I)-(MYJ)-Y(I))*Vs) 90 CONT INUE DO 10 L=5o100o5 WRITE (3,200) TG(L)oY(L)oX(L) WRITE (3,201) L 10 CONT INUE 30 CONT I NUE 100 FORIAT 101 FORMAT 200 FORNAT 201 FORMA T 400 FORMAT 401 FORMAT $' AS= 402 FORMAT $' Yo= 403 FORMAT( $F5o3 404 FORMAT 405 FORMAT $8 X, 'VT' 800 FORMAT CALL EX E IN D ( I 3 F10 04) 3F10.2) 30XF20.0,2F2083) I+' I120)

'O DELTA TIME ='lF6o4o' DELTA Z

'O ','DRIER VARIBLES DL='IF4al,' AG=

oF4 a2 o' W='F6.4)

'OGAS PROPERTIES DENG=',F64,'

oF6*4' T=' F4o0,' TW='sF40,o' H

0''5OLID PROPERTIES V=',F10s0o'

XC=' F5*3o' DENS=',F6@l) '0'0'CALCULATED CONSTANTS59F103) '0' 24Xo'GAS' 7X,'ZT'o8X,'G' 9X;'H' 9X 9X9 'ZW' tX I'VS') '1') =' F6.4) I oF4o2o CPG=' F ,4, EAT OF VAP=',F8.2) S= oF5t.09' XO='9 ' HW ' o 8X o ' oW ' FEAT U RE S ONE WORD IOCS SUPPORTED I N T E GE R S

CORE RECUIREMENTS FOR

CO 'MMN 0 VARIABLES 668 PROGRAM

END CF COMP IL A TTI // XEQ

(37)

// JOB T

LOG DRIVE CART SPEC

0000 02 CE

CART AVAIL PHY DRIVE

02CE 0000

V2 M12 ACTUAL 8K CONFIG 8K

// FOR

*IOCS( TYPEWRITER oKEYB 0ARD DISK CARDo1132PR INTER) *0NF WORD INTEGERS

*LIST SOURCE PROGRAM

C 9**t** ** * * * * ** **-M-** *** ** * ** *HN-*% HH * *HH

PROGRAl P

C C

C CONTINOUS DRYING UNDER

D IMENSION TG(100) p C READ CHARACTERISTICS OF C READ CHARACTERICS OF IN C LEAD CHARACTERICS OF IN C READ CHARACTERISTICS OF C READ CHARACTERICS OF TH READ (2,100) DLoA READ (2,100) DENG READ (2,100) DENS READ (2,101) VsSo READ (2,100) HVT

C INITIATE ARRAYS WITH IN

DO 20 K=l100 TG ( K )= T Y (K)=YO X (K) =XO 20 CONT INUE XC=0 .01

C CRITICAL MAOISTURE CONTE

C CALCULATE NFEDED CONSTA

DZ:!DL/99. NVC=0 60 CONT I NE NVC=NVC+1 IF (NVC-1000C) 11 1 CONT INUE

C PROPERTIES OF THE GAS GAS=AG*DENG*CPG ZT=DZ*DT G=AG*V*DENG H=0a01*G**0e 8 H H *W Z= GA S* D Z VT=DT*V*GAS ZW N =71 T *HW C RATIO OF MOISTURE OPTIMIZING VELOCITY ADIABATIC CONDITION Y(100) ,X(100) DRIER WDL AG

FLOWING GAS DENG*CPGYO

COMING SOLID DENSASXO TINE-VELOCITY VoSoDT E ENERGY (TEM"PERATURE) G W eCPGYO oASo X 0 DT ITIAL C HVoTWoT ONDITIONS XC FOR CALCULATIONS

M DENSITY PHEAT CAPACT IY ,AREA

VS= ( V*AG* DENG) / ( SA S*DENS)

WRITE (3,800)

DO 901 =1,99

J=I1+1

TG( J)=( (TG( J)*GZ)+( TG( I)*VT)+( T'*ZW) )/(GZ+VT+ZW)

TEAP=(TG( I)+TG(J) )/2a-TW

Y ( J ) =Y ( I) + ( (S*HW*TEMP*DT ) / ( HV*AG*DENG*V) X(J)=X(I)-( (Y(J)-Y(I))*Vs) IF (X(J)-XC) 95,9%590 CONT I NUE 95 K=J IF (K-99) 1010,99*1 1001 IF (K-99) 99,99,102 1010 V=V-100. GO TO 60 1020 V=V+100 GO TO 60 99 CONT INUE R ITE (3,400) DTDZ WRITE (3,401) DLAG WRITE (3,402) DENG, WRITE (3,403) VSoX WRITE (3,404) GAS Z WRITE (3,405) DO 10 L=5,100,5 WRITE (3,200) TG(L) WRITE (3,201) L 10 CONTINUE 001 0 oAS ,W CPGYOTTvHV 0,XCDENS T oGoHoHWGZ 9VT 0Z, VS ,Y(L) ,X(L) WRITE 100 FORMAT 101 FORMAT 200 FORMAT 201 FORMA T 400 FORMAT 401 FORMAT $' AS= 402 FORMAT S 1 YO= 403 FORMAT( SF5.3, 404 FORMAT 405 FORMAT $8X, 'VT' 00 FORMAT 501 FORMAT 505 FORMAT 80C FORMAT CALL EX END 3 9501) NVC (3 F 10 a 4) (3F10.2) (30XF.20o0,2F20.3) '+' , I20)

('o',' DELTA TIME =' ,F6.4,' DELT

'0','DRIER VARIBLES DL=',F4.1,'

,F4.2,' W=' F6 s4)

(10','GAS PROPERTIES DENG=',F6o4'

',F6.4,' T=',F4.09' TW ='.lF4*, ' '0','SOLID PROPERTIES V=',F10.0,' XC='oF5,3,' DENS=',F61) ('' ,'CALCULATED CONSTANTS',9E10&3) ('0' 24X, 'GAS' , 'ZT' ,8X, 'G' ,9X,'H'*X, ,RX, 'Z'' ,SX, 'VS1 ) (' ',20X,'V=',F10.o0,10X,1) (' 1,I6) ('1') IT A Z =' ,F6o4) AG=',F4.2, CPG=',F6.4, HEAT OF VAP=',F8.2) S= ,F5e,0 ' X ='0 ,9X, 'HW' ,8X, 'GM' UNREFERENCED STATEMENTS 500 505

(39)

// JOB T

LOG DRI\VE

0)0 0

CART SPEC

02CE

CART AVAIL PHY DRIVE

02CE 0000

212 f ,-CTUAL 0K CONFIG RK

// FOR

*IOCS (TYPEWR ITER t KEYBOARD oD ISK 9CARDo 113 2PRI INTER

*ONE WORD INTEGERS

*LIST SOURCE PROCGRAY

C ******* C

PROGRAM C TEMPERATURE DEPENDENCE

D ND ITION

C C

C CONTINOUS DRYING UNDER ADIABATIC C

DIMENSION TG(100),Y(100),X(1W

C READ CHARACTERISTICS OF DRIER WD C READ CHARACTERICS OF IN FLOWING GA

C READ CHARACTERICS OF IN COMING SOL C READ CHARACTERIC5 OF THE ENERGY (T

C READ CHARACTERISTICS OF TIME-VELOC

READ (2,100) DLAGV

READ (2,100) DENGCPGoYO

READ (2 100) DENS*ASoXO

READ (2,101) VoSqDT

C INITIATE ARRAYS WITH INITIAL CONDI DO 12 KL=1,100

READ (2#700) TG(KL)oY(KL)oX(

12 CONT INUE XC=C .01

C CRITICAL MOISTURE CONTENT XC

C CALCULATE NEEDED CONSTANTS FOR CAL

DZ=DL/99e

C PROPERTIES OF THE GAS STREAM DENS

GAS=AG*DENG*CPG 7Z T = 2*Z T c A C * V * D EN G H=0 .1*G**0a 8 HW=H-*W LAG S DENG9CPGpYO ID DENSoASoXO EMPERATURE) ITY VS*DT HVoTWT T IONS KL) CU LA T INS ITY oHEAT GZ=GA5*DZ VT=DT*V* GAS ZW= T*HW

C RATIO OF MOISTURE IN GAS AND SOLID FLOWS

VS= (V*AG*DENG) / ( S*AS*DENS)

WRITE (39404) GAS ZT GsH HWoGZ VT ZW *VS

W%RlITE (3#405)

WRITE (3,800)

DO 40 NDT=195

C READ CHARACTERISTICS OF IN COMING TEMPERATURES

READ (2*100) HVTWoT

TG (1) =T

CAPACTIYAREA

TG(1) oTN*HV

RITE (3,301) NDT ,,ITE (3,400) DToDZ WRITE (39401) DLsAGoASW RIT (39402) DENGCPGoYOoToTJHV WRITE (3,403) VSoX0,XCoDENS D0 90 I=1099 TG ( J)= ( ( TG ( J ) *GZ) + ( TG( I) *VT)+( TW*ZW) ) / TEFP= ( TG(I)+TG( J) ) /2 . TW J=I+1 Y ( )=Y ( I) + ( ( STHW TEMP* T ) / X ( J)=X (I)-( (Y (J)-Y (I) )*"VS)

90 CONT INUE

DO 10 L=5,100,5

4 RITE (3o200) TG(L)oY(L)oX(L)

RITE (3,201) L 10 C0NT IN'UE NV C=0 60 CONT I NUE NV C= NV C + 1 IF (NVC-10000) 70o70,95 70 CONT INUE

C RECALCUILATET ALL \/ELOCITY DEPENDENT

G=AG* ID ENG

H=O ,01*G**0 8

H C I= - C

V T-T VG A S

Z 7=ZT*HW

VS= (v*AG*DENGC) / ( S*A S*DENS)

ITE (3,500) V NVC D 0 8 0 MqP9 N =+1 T EMP=(T ()TG(Z)/2-TW Y ( N) =Y (M)+ ( ( S*H*T EMP* T ) / X (N =X( )-( (Y N -Y M ) VS) IF (X(N)-XC) 81 p1,80 80 CONT INuE GO TO 1020 81 KN (HV* GZ+VT+ZW) AG*DENG*V) CoNSTANTS T)+( T;*Zi) ) / ( Z+VT+Z ( HV*AG*DENG*V) ) IF (K-98) 1010,85o85 85 IF (K-99)C5c95'020 10 10 V V-10 0 GO TO 60 1020 V= V+10 0 o GO TO 60 95 CONT INUE WR ITE (3505) SITE ( 3 *801) W ITE (3,801) DC 20 KL=5,100,5 WRITE (3,200) TG(KL)oY(KL)oX(KL) WRITE (3o201) KL 20 CONT INUE (41)

PA G E- 3 RITE (3,501) NVC 40 CONTINUE 100 FORMAT 101 FORMAT 200 FORMAT 201 FORA T 301 FQ 0AT 400 FORMAT 401 FORYA T $1 AS= 402 FORMAIAT 403 FORMA T( SF5.3,' 404 FOR AT 405 FOR'MA T $SXo'VT' 500 FORMiA T 501 505 700 So 801 3F10 /4) 3F10a2) 30 X , F 20 9 FORMA T FOR MAT FORM AT FOPMAT FORMAT CALL EXI END s0o 2F20o 3*) '+' 120 )

'1' ,'THIS IS NEW DATA SET' , I

'0'' DELTA TIME

='IF6.4o'

'O' IO'DRILER VAR IBLES DL=' eF4*l o '

oF4a2,' W='F6.4)

'0 ' 'GAS PROPER TIES DENG ' F6 * 4 o

VF6.4, T='F4a 0 s' TW =IF4,O

0 ' 9' SOL ID PROPERT IES V= o F10a 0 s

XC=' F5.3, DENS=' ,F6a1)

'0' 'ICALCULATED CONSTANTS' 9E1093)

'0 ' 24X , 'GAS' ,7X, 'ZT' o8X, 'G',9Xo 'H

EX, 'ZW' ,8X.'VS') '20X, ' V=' o F10 00 91(X o I10) ' 6) '0' ,45Xo'TG' 18X I'Y'19X9'X') F6.02F6.3) '1') T 10) TA Z =',F6.4) AG=' F4e 2s CPG=' ,F6a49 HEAT OF VAP='F8.2) S=' F5*0 ' XO=' ' ,9X e 'HW' ₉ X ' G ' FEATURES ONE WI0D IOCS SUPPORTED INTEGEGS

CORE rECUIREENTS FOR

COMMON 0 VARIABLES 672 PROGRAM

END OF COMPILATION

// XEC

(42)

Bird, R. Byron; Steward, Warren E.; Lightfoot, Edwin N,;

Transport Phenomena, Copy. 1965, John Wiley & Son, Inc.

New York

Carnahan, Brice; Cuther, H. A.; Wikes, James 0.; AD-plied Numerical Methods, John Wiley & Son, Inc., New York, copy.

Chung, Sen F., "Mathematical Model and Optimization of Drying Process for a Through-Circulation Dryer",

The Canadian Journal Of Chemical Engineering, Vol. 50

October, 1972

Harbert, F. C., "Temperature Differences Give Automatic

Control of Process Plant Dryers", Process Engineer, Vol. 122 September, 1973

Keey, R. B., Drying Principles and Practice, Pergaman Press, New York, 1972

Nonhebel, G.; Moss, A. A. H., Drying of Solids in The Chemical Industry, Butterworth & Co., Ltd., London, 1971 Novak, Lawrence T.; Coulman, George A., "Mathematical Models for The Drying of Rigid Porous Materials",

The Canadian Journal of Chemical Enn, Vol. 53,

February, 1975

Perry, Robert H., (Editor),,Perry's Chemical Engineers' Handbook, McGraw-Hill Book Company, New York, 1963.

Shinskey, F. Greg, Humidity and Dryer Control, The Foxboro

Co. Publication 41₃ -6, Foxboro, MA

Treybal, Robert E., Mass-Transfer _perations, McGraw-Hill Book Co., New York, 1955